Multifrequency Backscattering Tomography: Extension to the Case of a Vertically Varying Background

The distortion and limited resolution of the image are serious problems of single-frequency diffraction tomography. Multlfrequency methods, such as the multifrequency backscattering tomography, can improve the resolution and image quality significantly. In this work, we extend the multifrequency backacattering tomography to the case of vertically varying background. The image reconstruction formula has the same form as that in constant background except for a phase factor in the backpropagator. The computation speed of the image reconstruction by backpropagation is almost the same as in the case of constant background. Numerical tests show superior resolution and image quality. Examples are also given to demonstrate the necessity of using the reconstruction formula of vertically varying background in the corresponding cases.